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Math Help - How to calculate min acceleration between two points of different velocities

  1. #16
    MHF Contributor ebaines's Avatar
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    Re: How to calculate min acceleration between two points of different velocities

    Quote Originally Posted by calltronics View Post
    Please see comments in your answer.
    Starting with
     a= \frac {v_c-100}t

    and

    a = \frac {40-v_c} {2-t}

    set them equal, cross-multiply, and manipulate to get  v_c by itself:

    \frac {v_c-100} t = \frac {v_c-40}{2-t}\\v_ct - 40 t = (v_c-100)(2-t)\\v_c(2t-2)=-200+40t\\v_c=\frac {200+140t}{2t-2} = \frac {100+70t}{t-1}
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  2. #17
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    Re: How to calculate min acceleration between two points of different velocities

    Thank you, it is so easy when you can see it.
    I appreciate your patience
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  3. #18
    MHF Contributor ebaines's Avatar
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    Re: How to calculate min acceleration between two points of different velocities

    Quote Originally Posted by calltronics View Post
    The total time is now the variable.
    The acceleration is fixed at 0.7m/s^2
    Same type of solution Passing through "Point C".
    Solved for either t1 or t2 as a minimum total time.
    If you set a = 0.7m/s^2 and solve for t1 and t2 then the result is:

    t1 = 0.5208 seconds
    d1 = 0.147m
    v_c = 0.464 m/s
    t2 = 0.6065 seconds
    d2 = 0.153m
    T_total = 1.127 second

    In reviewing my previous posts with the solution to your first question I see that I made a typo, which I have corrected in bold font below:

    Quote Originally Posted by ebaines View Post
    Apply the quadratic equation to solve, and you find that t = 0.818665 seconds. This yields a = 0.165 m/s^2, point c at 0.137m, and v_c = 0.235m/s.
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  4. #19
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    Re: How to calculate min acceleration between two points of different velocities

    wow glad you spotted that I am going to motion trials tomorrow.
    Bit of difference between 0.818 m/s^2 and 0.818s
    Thing is without thinking I used the result as acceleration and calculated the time and distance from it.
    It was movable and never hit limits.
    I never twigged but might have tomorrow when the machine pulled itself off the floor!
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